On the Concavity of Tsallis Entropy Along the Heat Flow
MCML Authors
Abstract
Abstract
We demonstrate the concavity of the Tsallis entropy along the heat flow for general dimensions, expanding upon the findings of Wu et al 2025 and Hung 2022, which were previously limited to the one-dimensional case. The core of the proof is a novel estimate of the terms in the second-order time derivative, and a rigorous validation of integration by parts. The resulting bound establishes a new functional inequality, which may be of interest for other areas of mathematical analysis.
BibTeXKey: Sun26